Objects in animation moving at different speeds on the same keyframe
You could parent the pearls to the crown, so that they follow the crown without being animated.

To do this, select the pearls and then the crown (so that the crown is active), and press CtrlP. Now you only have to animate the crown.



As for the reasons why the objects are out of sync in the first place, my first guess is that the origins are not in the same place.